Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C5 |
| direct product | C7×C5⋊D385 |
| unambiguous semidirect product | C5⋊(C7×D385) |
| unambiguous semidirect product | C7⋊(C7×C5⋊D55) |
| unambiguous semidirect product | C11⋊(C7×C5⋊D35) |
| Fitting, socle, Hall | C52×C72×C11 ⋊ C2 |
| derived | C52×C7×C11 ⋊ C2×C7 |
| Hall | C52×C72 ⋊ D11 |
| Hall | C72×C11 ⋊ C5⋊D5 |
| Hall | C52×C11 ⋊ C7×D7 |
| Sylow | C72 ⋊ C5⋊D55 |
| Sylow | C52 ⋊ C7×D77 |
| Sylow | C11 ⋊ C7×C5⋊D35 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C5⋊D385 |
| commutator, cosocle, hypocenter | C52×C7×C11 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72×C11 | C2 |
| LCS | G ▷ C52×C7×C11 | |
| UCS | C1 ◁ C7 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3850 |
6748 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 78);